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A sequence of non-zero real numbers is such that every term after the

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A sequence of non-zero real numbers is such that every term after the  [#permalink]

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New post 09 Jun 2018, 11:17
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A sequence of non-zero real numbers is such that every term after the first term, is half of its previous term. What is the fifth term of this sequence?

(1) Product of fourth and sixth terms of this sequence is twice the fifth term.

(2) Sum of third and fourth terms of this sequence is six times the fifth term.
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A sequence of non-zero real numbers is such that every term after the  [#permalink]

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New post 09 Jun 2018, 12:44
amanvermagmat wrote:
A sequence of non-zero real numbers is such that every term after the first term, is half of its previous term. What is the fifth term of this sequence?

(1) Product of fourth and sixth terms of this sequence is twice the fifth term.

(2) Sum of third and fourth terms of this sequence is six times the fifth term.


Let the non-zero real numbers are \(a_1, a_2,.......,a_{n-1},a_n\).
Given:- \(a_n=\frac{a_{n-1}}{2}\) or\(a_{n-1}=2a_n,\) n>1
Question stem:- \(a_5=?\)

statement1,

Given,\(a_4*a_6=2a_5\)
Or, \(2a_5*\frac{a_5}{2}=2a_5\)
Or, \(a_5=2\) (since the terms in the sequence are non-zero real numbers)
So, sufficient.

statement2, Given,\(a_3+a_4=6a_5\)
Or,\(2a_4+2a_5=6a_5\)
Or,\(a_4=2a_5\),
Or, \(a_5\)=\(\frac{a_4}{2}\) ;this is nothing but the re-statement of the data given in the question.
Hence, insufficient.

Ans. A
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Re: A sequence of non-zero real numbers is such that every term after the  [#permalink]

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New post 12 Jun 2018, 23:02

Solution



Given:
    • In a sequence of non-zero real numbers, every term after first term is half of its previous term

To find:
    • The fifth term of the sequence

Analysing Statement 1

    • As per the information given in statement 1, product of fourth and sixth terms is twice the fifth term

If we assume fourth term to be 4x, then fifth term will be 2x and sixth term will be x
As per the statement,
    • 4x * x = 2 * 2x
    Or, \(4x^2 = 4x\)
    Or, x = 1 (as x is non-zero)

Therefore, we can find the value of the fifth term

Hence, statement 1 is sufficient to answer

Analysing Statement 2

    • As per the information given in statement 2, sum of third and fourth terms is six times the fifth term

If we assume the third term to be 4y, then fourth term will be 2y and fifth term will be y
As per the statement,
    • 4y + 2y = 6 * y
    Or, 6y = 6y

We don’t get any solution from this equation

Hence, statement 2 is not sufficient to answer

Hence, the correct answer is option A.

Answer: A
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Re: A sequence of non-zero real numbers is such that every term after the &nbs [#permalink] 12 Jun 2018, 23:02
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